Default gateway not available

My Win7 computer periodically loses network connectivity. This occurs from every five minutes to once or twice a day. The troubleshooting option of the Network icon in the System area goes through the process and then the problem is fixed - until the next time. The problem is listed as "Default gateway not available." with the notation "Fixed". I have Googled this and found many others with the same problem, but nobody has suggested a fix that works for me.
I am using the latest drivers for my motherboard Realtek PCIe GBE Family Controller. This computer is connected by cable to my router (Linksys WRT54G). All other non-Win7 computers, wireless and wired, remain on the network.
Any suggestions?

Thanks for the two responses.
The answers to the posed questions:
Win7 SP-1 is installed, but the problem appeared already before that.
The cable is fine and works with other computers. I will try another cable, but there were no such problems with the XP computer which was in this location and used the same cable.
I am using the AVG paid version for anti-virus and ZoneAlarm as the firewall. The other computers (XP and Vista, wired and wireless, using the same versions of these work fine.
I am not using Homegroups at all. IPv6 is enabled, however.
The router is supplying the default gateway correctly to all the computers. It is only the Windows 7 which loses the gateway.
Since almost all the published complaints about this error message refer to Windows 7 I assume that it is an issue with the OS and not hardware.
Thanks for the responses!

Three things to try:
1. Disable Zonealarm.
2. Check to see if your router has any firmware updates avaiable.
3. Disable IPV6. You have no need for it at this time unless you are running widows 7 Homegroups which only works with an all windows 7 network.